Question: Umaima is 4 years older than Emily. Eight years ago, Umaima was 5 times as old as Emily. How old is Emily now?
Explanation: We can use the given information to write down two equations that describe the ages of Umaima and Emily. Let Umaima's current age be $u$ and Emily's current age be $e$ The information in the first sentence can be expressed in the following equation: $u = e + 4$ Eight years ago, Umaima was $u - 8$ years old, and Emily was $e - 8$ years old. The information in the second sentence can be expressed in the following equation: $u - 8 = 5(e - 8)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $e$ , it might be easiest to use our first equation for $u$ and substitute it into our second equation. Our first equation is: $u = e + 4$ . Substituting this into our second equation, we get the equation: $(e + 4)$ $-$ $8 = 5(e - 8)$ which combines the information about $e$ from both of our original equations. Simplifying both sides of this equation, we get: $e - 4 = 5 e - 40$ Solving for $e$ , we get: $4 e = 36$ $e = 9$.